Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<vector>
using namespace std;
double find(int A[],int n,int i,int j){
    double sum=0;
    int cnt=0;
    for(int k=n-1;k>=0;k--){
        if(k==i||k==j) continue;
        sum+=A[k];
        cnt++;
        if(cnt>=2) break;
    }
    return sum;
}
int main(){
    int n,A[1010];
    cin>>n;
    for(int i=0;i<n;i++){
        cin>>A[i];
    }
    sort(A,A+n);
    double ans=0;
    for(int i=0;i<n-1;i++){
        for(int j=i+1;j<n;j++){
            double a=A[j]-A[i];
            double b=find(A,n,i,j);
            ans=max(ans,b/a);
        }
    }
    printf("%.20lf\n",ans);
    return 0;
}